The Observer-State Problem

The essence of research at ASPL is the observer-state problem.  That is, we are first interested in the state (or states) x of some stochastic process, with correlative structure Φ and stochastic input w.  The process evolves over a recursion index s  that may represent increments in time, space, or scale.  We initially specify the process in terms of an a priori stochastic model θ.  Since we do not generally know the true value of the state, we attempt to observe it with sensors (possibly different sensors at multiple resolutions).  The quantities measured by the sensors typically are not precisely the state parameters of interest.  The observations y are therefore related to the state parameters through a mapping function H and sensor-dependent noise v.  With the model and the observations in hand, we may then attempt to estimate the state parameters conditioned on particular optimality criteria.  The estimator produces estimates of the state x, but may also output information about the estimate error and probabilities of different signal states.  Estimator outputs are compared with their expected theoretical behavior, training data, or independent in situ measurements in order to verify the estimator accuracy.  The divergence between the estimates and the verification data constitutes an error signal ε that can be presented to system-theoretic or information-theoretic learning algorithms that update or otherwise improve the underlying stochastic model by providing a posteriori estimates P(θ|Y,ε,α) of model parameters, given the observation record Y,ε, and other estimator performance measures α. 

 A Multidisciplinary Approach

The report by The Boyer Commission on Educating Undergraduates in the Research University concluded that, "Unfortunately, research universities are often archipelagos of intellectual pursuit rather than connected and integrated communities.” [Boyer, (1998)].  The disconnection described in this report stifles the great potential synergy between engineering and the earth sciences.  The research at ASPL resides at the intersection of engineering and earth science, thus providing many opportunities for students to build connections between these disciplines. 

References

 [Boyer, (1998)] Boyer Commission on Educating Undergraduates in the Research University, “Reinventing Undergraduate Education: A Blueprint for America's Research Universities,” Carnegie Foundation, 1998.